some data from table categories:
(category_id, name, left_node, right_node)

1	 struktura 	1 52
9 	radius nautica 	4 17
11 	skola jedrenja 	7 14
21 	asda 		8 11
22 	daaada 		9 10


----
php: 

$iterator = new RecursiveIteratorIterator(new recursiveArrayIterator($hierachy->SinglePath($node)));
try {
    foreach($iterator as $key=>$value)
        {
        echo $key.' -- '.$value.'<br />';
        }
    }
catch(Exception $e)
    {
    echo $e->getMessage();
    }
------

returns: 

name -- struktura
name -- skola jedrenja
name -- daaada
name -- radius nautica
name -- asda

which is wrong order, why?

It looks to me that query in method SinglePath() is wrong but i am not sure, here is the query:

SELECT parent.name FROM categories AS node, categories AS parent WHERE node.left_node BETWEEN parent.left_node AND parent.right_node AND node.name = '{$node_name}' ORDER BY node.left_node